The processing of analog signals often requires circuits which can output a proportional signal to the product of two analog input signals.
Such circuits are commonly termed analog multipliers. For example, analog multipliers are used for balancing modulators, as well as in phase detectors and the like devices. With digital signal converters having a quadratic type of transfer function, it is essential that an analog multiplier be employed to produce a proportional signal to two analog input signals which are identical with each other.
A large number of analog multipliers are based on an exponential transfer function of bipolar transistors (BJTs). Actually, a differential stage with coupled emitters may constitute an elementary multiplier cell capable of generating (differential) collector output currents which are dependent on a differential voltage applied to its inputs, e.g., to the base terminals of a bipolar transistor pair forming the differential stage.
By duplicating an elementary cell, analog multipliers can be obtained which can operate between two or among four quadrants of a differential plane of input voltages.
A typical cell of a four-quadrant multiplier is referred to in the literature as Gilbert's cell or circuit.
A reference for this circuit structure is, for example, IEEE Journal of Solid-State Circuits, vol. sc-19, No. 6, December 1974, New York, U.S.A., pages 364-373, Berrie Gilbert “A High-Performance Monolithic Multiplier Using Active Feedback.”
In multipliers of this kind, an expedient is often resorted to in order to reduce the error introduced by non-linearities of the circuit. Briefly, a pre-distortion stage is connected in, upstream of the analog multiplier, to introduce pre-distortion in the input signal and compensate for the hyperbolic tangent transfer characteristic of the multiplier cell.
The pre-distortion stage is usually in the form of a diode-configured bipolar transistor whereby a current input signal is forced to produce a voltage output signal having a transfer function which is the reciprocal of the hyperbolic tangent.
Multipliers of this type are known in the literature, e.g., from a book “Analog Integrated Circuits—Analysis and Design” by Paul R. Grey and Robert G. Meyer, McGraw-Hill, which contains a detailed description and an analysis of these circuits under Chapter 10, pages 694-705.
The basic characteristics expected of an analog multipliers include: high accuracy, relatively low power consumption, and moderate circuit complexity.
However, obtaining one of these characteristics sometimes involves the need for a trade-in with one or all of the other characteristics.
In particular, the prior analog multipliers mentioned above cannot be implemented with low supply voltages.
Also, the common mode output voltage varies as the potential at a central node of the multiplier, which potential is equal to the half sum of the inputs, and this makes conventional multipliers too readily affected by sharp variations in the input signal.
Finally, the accuracy of DC gain is dependent on the value of I of the bias generators.